For different reasons, it is normal to provide absorbent sanitary articles, such as sanitary napkins, diapers and incontinence guards, with elastic elements. For instance, diapers are nearly always provided with so-called leg elastic which functions to provide sealing abutment of the diaper casing sheet with the thighs of the wearer. Elastic elements are also often used to give sanitary articles or parts of such articles a desired shape, and also to provide waist elastic. Elastic is also used to raise liquid barrier forming parts of the article, to prevent liquid from spreading across the outer sheet of the article. Absorbent sanitary articles of the aforesaid kind are produced in a continuous process line, in which a web of material, that normally forms the outer backing sheet of the article, travels continuously through the process line in successive stages which include the application of absorbent bodies and the application of further surface sheets or layers and elastic elements. The individual articles are cut from the continuous composite web in the final stage of such a process line. The elastic elements are most often mounted in a pre-stretched state, i.e. have been stretched from a rest state to which they strive to return. So that the pre-stretched elastic elements will not contract and therewith gather together or pucker the material to which they are fastened, the elastic elements are maintained in a stretched state until the final stage of the manufacturing process. This can be readily achieved with elastic elements that extend across the full length of the article in the movement direction of the process line. However, in the case of elastic elements that are active across only a part of the length of the article in the movement direction, a problem arises in retaining the elements in a pre-stretched state without complicating the process and/or without mounting functionally inactive parts of elastic elements on the web in the article manufacturing process. A solution to this problem is proposed in Swedish Patent Application No. 9602131-6 filed on May 31, 1996.